On the anti-forcing number of benzenoids
WebThe anti-forcing number of G is the smallest number of edges whose removal from G results in a subgraph with a unique perfect matching, denoted by of (G). In this paper, we obtain that for a (3, 6)-fullerene graph G, f (G) >= 1 and af(G) >= 2, and any equality holds if and only if it either has connectivity 2 or is isomorphic to K-4. WebThe anti-forcing number is introduced as the smallest number of edges that have to be removed that any benzenoid remains with a single Kekul´e structure. Similarly, the anti- Kekul´e number is discussed as the smallest number of edges that have to be removed that any benzenoid remains connected but without any Kekul´e structure. These …
On the anti-forcing number of benzenoids
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Web470 . C. Larson and N. Van Cleemput, Forcing Independence Croat. Chem. Acta. 86 (2013) 469. that molecular resonance energy of a sample of ben-zenoids correlates strongly with the Web5 de jul. de 2016 · In particular, for all benzenoid systems, recently Xu et al. [22] showed that the maximum forcing number is equal to the Clar number, and Lei et al. [13] showed that the maximum anti-forcing number is equal to the Fries number. Both indices can measure the stability of benzenoid hydrocarbons. We may refer to a survey [2] on this topic.
WebLet G be a (4,6)-fullerene graph. We show that the maximum forcing number of G is equal to its Clar number, and the maximum anti-forcing number of G is equal to its Fries number, which extend the known results for hexagonal systems with a perfect ... WebPreviously introduced concepts the anti-Kekule number and anti-forcing number (Vukicevic et al., J. Math. chem., in press) are applied to cata-condensed benzenoids. It is shown that all cata-benzenoids have anti-Kekule number either 2 or 3 and both classes …
WebG−S has a unique perfect matching. The cardinality of a smallest anti-forcing set is called the anti-forcing number of G, denoted by af(G). D. Vukiˇcevi´c and N. Trinajsti´c [12, 13] recently introduced the anti-forcing number of graphs and determined the anti-forcing numbers of parallelogram benzenoid and cata-condensed benzenoids. Web5 de jul. de 2016 · In particular, for all benzenoid systems, recently Xu et al. [22] showed that the maximum forcing number is equal to the Clar number, and Lei et al. [13] showed that the maximum anti-forcing number is equal to the Fries number. Both indices can measure the stability of benzenoid hydrocarbons. We may refer to a survey [2] on this topic.
WebWe show that the maximum forcing number of G is equal to its Clar number, and the maximum anti-forcing number of G is equal to its Fries number, which extend the known results for hexagonal systems with a perfect matching (Xu etal., 2013; Lei etal., 2016).
WebWe define the anti-forcing number of a perfect matching M of a graph G as the minimal number of edges of G whose deletion results in a subgraph with a unique perfect matching M , denoted by a f ( G , M ) . The anti-forcing number of a graph proposed by ... green thuja for saleWebe number either 2 or 3 and both classes are characterized. The explicit formula for anti-forcing number of chain (unbranched) cata-benzenoids is given. It is also shown that anti-forcing number of any cata-benzenoid goes up to h/ 2w hereh is the number of … fnb the entertainerWebFor individual Kekule valence structures we consider the smallest possible number of placements of CC double bonds such that a Kekule structure is fully determined. The number may be viewed as special weighting scheme for individual Kekule valence structures. Alternatively its reciprocal indicates the degree of a long-range order in a … fnb the grove home affairsWeb1 de mar. de 2016 · We define the anti-forcing number of a perfect matching M of a graph G as the minimal number of edges of G whose deletion results in a subgraph with a unique ... br000135 D. Vukičević, N. Trinajstić, On the anti-Kekulé number and anti-forcing … fnb the grove branchWeb18 de dez. de 2024 · The initial set S is called a forcing set (zero forcing set) of G if, by iteratively applying the forcing process, every vertex in G becomes colored. The zero forcing number of G, denoted Z(G), is the minimum cardinality of a zero forcing set of … fnb the groveWebAnti-Kekulé numbers of some chemical graphs were studied, such as a hexagonal system [ 3], the infinite triangular, rectangular and hexagonal grids [ 16], cata-condensed benzenoids [ 18], fullerene graphs [ 20] and cata-condensed phenylenes [ 22]. fnb the grove home affairs bookingWeb13 de jun. de 2006 · The anti-forcing number is introduced as the smallest number of edges that have to be removed that any benzenoid remains with a single Kekulé structure. Similarly, the anti- Kekulé number is discussed as the smallest number of edges that … green thumb 12\\u0027 fiberglass pole tree trimmer